Journal of Guangxi Normal University(Natural Science Edition) ›› 2012, Vol. 30 ›› Issue (4): 42-47.

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Pulse Control and Bifurcation Analysis of a SIRS Epidemic Model with Vertical Transmission

HAO Li-jie, JIANG Gui-rong, LU Peng   

  1. School of Mathematics and Computing Science,Guilin Universityof Electronic Technology, Guilin Guangxi 541004,China
  • Received:2012-07-26 Published:2018-11-27

Abstract: In this paper,the dynamical behavior of a SIRS epidemic model with birth pulse,pulse vaccination and vertical transmission are studied.The condition ofexistence for supercritical bifurcation is derived,and then the threshold for adiseaseto be extinct or endemic is established.The Poincaré map and center manifold theorem are used to discuss flip bifurcation of endemic periodic solution.Numerical results for periodic solutions and bifurcation diagrams,which are illustrated with an example,are in good agreement with the theoretical analysis.

Key words: SIRS epidemic model, vertical transmission, pulse vaccination, threshold, bifurcation

CLC Number: 

  • O175.1
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